Details

sample138.0ms

Algorithm

intervals

Results

63.0ms	256×	body	80	valid
39.0ms	237×	body	80	nan

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
4	1440
3	365
2	102
1	50
0	28

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize89.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a))
0.3b	(/ (/ 2.0 t) 3.0)
2.9b	(fma (- c b) (- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a)) (/ (sqrt (+ a t)) (/ t z)))
6.7b	(/ (sqrt (+ a t)) (/ t z))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

548×	`times-frac`
469×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
347×	`add-cube-cbrt`
220×	`prod-diff`
131×	`associate--r+`
56×	`sqrt-prod`
41×	`difference-of-squares`
34×	`div-inv`
20×	`associate-/l*`
16×	`associate-/r*` `distribute-lft-out--`
14×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
13×	`fma-neg`
9×	`add-log-exp`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`diff-log` `associate-/l/`
2×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `sqrt-div` `frac-sub` `flip--`
1×	`flip3-+` `associate-/r/` `flip-+` `fma-udef` `associate--r-`

Counts

4 → 473

Calls

4 calls:

74.0ms	(- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a))
16.0ms	(/ (/ 2.0 t) 3.0)
0.0ms	(fma (- c b) (- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a)) (/ (sqrt (+ a t)) (/ t z)))
14.0ms	(/ (sqrt (+ a t)) (/ t z))

series408.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a))
19.0ms	(/ (/ 2.0 t) 3.0)
261.0ms	(fma (- c b) (- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a)) (/ (sqrt (+ a t)) (/ t z)))
104.0ms	(/ (sqrt (+ a t)) (/ t z))

simplify3.0s

Counts

485 → 485

Iterations

Iter	Nodes
done	5000
2	4831
1	2125
0	874

prune5.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
2.6b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
3.5b	(/ (* z (sqrt (+ t a))) t)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-cbrt-cube` `add-exp-log`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r` `sqrt-div` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `associate-*l/` `associate--l+` `unswap-sqr` `associate-/l/`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 183

Calls

4 calls:

16.0ms	(* z (sqrt (+ t a)))
7.0ms	(/ 2.0 (* t 3.0))
50.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
26.0ms	(/ (* z (sqrt (+ t a))) t)

series527.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* z (sqrt (+ t a)))
38.0ms	(/ 2.0 (* t 3.0))
278.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
126.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.9s

Counts

195 → 195

Iterations

Iter	Nodes
done	5001
1	1415
0	491

prune2.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
0.2b	(/ (sqrt (+ t a)) t)
0.3b	(/ 2.0 (* t 3.0))
2.3b	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
56×	`prod-diff`
54×	`add-cube-cbrt`
48×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
19×	`distribute-lft-out`
16×	`sqrt-prod`
13×	`add-cbrt-cube` `add-exp-log`
10×	`div-inv` `associate-/l*`
8×	`frac-times` `flip3--` `flip--`
6×	`pow1` `associate-r` `frac-sub`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-/r` `flip3-+` `associate-r/` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
2×	`clear-num` `sub-neg` `frac-2neg` `sqrt-div` `associate-*l/` `prod-exp` `associate--l+` `cbrt-unprod` `difference-of-squares` `associate-/l/`
1×	`pow-prod-down` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 185

Calls

4 calls:

167.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
23.0ms	(/ (sqrt (+ t a)) t)
13.0ms	(/ 2.0 (* t 3.0))
1.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
99.0ms	(/ (sqrt (+ t a)) t)
32.0ms	(/ 2.0 (* t 3.0))
302.0ms	(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify2.2s

Counts

197 → 197

Iterations

Iter	Nodes
done	5028
2	3480
1	983
0	399

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 2.0 t) 3.0)
2.9b	(fma (- c b) (- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a)) (posit16->real (real->posit16 (/ (sqrt (+ a t)) (/ t z)))))
6.7b	(/ (sqrt (+ a t)) (/ t z))
53.6b	(posit16->real (real->posit16 (/ (sqrt (+ a t)) (/ t z))))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

238×	`times-frac`
158×	`*-un-lft-identity`
130×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`sqrt-prod`
20×	`associate-/l*`
16×	`associate-/r*`
14×	`add-cbrt-cube` `add-exp-log` `div-inv` `distribute-lft-out`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`flip3-+` `associate-/r/` `flip-+` `fma-udef` `remove-posit16`

Counts

4 → 226

Calls

4 calls:

15.0ms	(/ (/ 2.0 t) 3.0)
0.0ms	(fma (- c b) (- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a)) (posit16->real (real->posit16 (/ (sqrt (+ a t)) (/ t z)))))
409.0ms	(/ (sqrt (+ a t)) (/ t z))
0.0ms	(posit16->real (real->posit16 (/ (sqrt (+ a t)) (/ t z))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (/ 2.0 t) 3.0)
280.0ms	(fma (- c b) (- (/ 5.0 6.0) (- (/ (/ 2.0 t) 3.0) a)) (posit16->real (real->posit16 (/ (sqrt (+ a t)) (/ t z)))))
89.0ms	(/ (sqrt (+ a t)) (/ t z))
104.0ms	(posit16->real (real->posit16 (/ (sqrt (+ a t)) (/ t z))))

simplify2.1s

Counts

238 → 238

Iterations

Iter	Nodes
done	5001
2	2624
1	1032
0	431

prune3.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes1.2s

Accuracy

-19.5% (1.8b remaining)

Error of 2.5b against oracle of 0.7b and baseline of 2.2b

bsearch742.0ms

Steps

Iters	Range		Point
10	7.203812753580602e-282	9.380270591597068e-268	5.358377107920803e-277
10	-6.392896559112743e-238	-1.0097446013295498e-255	-5.0089747297515344e-254

simplify39.0ms

Iterations

Iter	Nodes
done	70
2	70
1	68
0	52

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.9s	7910×	body	80	nan
2.3s	8000×	body	80	valid